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Why do we always characterize a LTI system by its impulse response?
An arbitrary input can be seen as the sum of weighted and time-delayed impulses. Because the systems is Linear Time Invariant (LTI) the output is simply obtained summing the weighted and time delayed versions of the impulse response. The weighting and time delay factors are exactly the same as those used in obtain the input signal from an impulse.
Which is an important property of an LTI system?
The impulse response is an especially important property of any LTI system. We can use it to describe an LTI system and predict its output for any input. To understand the impulse response, we need to use the unit impulse signal, one of the signals described in the Signals and Systems wiki.
How is output of a discrete time LTI system determined?
The output of a discrete time LTI system is completely determined by the input and the system’s response to a unit impulse. Figure 4.2. 1: We can determine the system’s output, y [ n], if we know the system’s impulse response, h [ n], and the input, x [ n].
Which is the output of an impulse response?
Figure 4.2. 1: We can determine the system’s output, y [ n], if we know the system’s impulse response, h [ n], and the input, x [ n]. The output for a unit impulse input is called the impulse response.
Which is an example of the unit impulse response?
The only non-obvious step is that we must represent the unit step response in a functional form . Some examples will clarify. Consider the systems shown below. In the circuit the input and output are e in and e out, respectively. In the mechanical system the input and output are x in and x out, respectively.
What is the output of an impulse signal?
The output for a unit impulse input is called the impulse response. Since we are considering discrete time signals and systems, an ideal impulse is easy to simulate on a computer or some other digital device. It is simply a signal that is 1 at the point n = 0, and 0 everywhere else.